Question

Прямоугольник ABCD разделили на четыре меньших прямоугольника с одинаковыми периметрами.Известно,что АВ 18см ,а ВС 16см.Найдите длины сторон остальных прямоугольников.Объясните ответ.

Answer 1

На рисунке приложения даны два варианта ответа. 
Периметр - сумма длин всех сторон многоугольника. 
Общие стороны фигур считаются отдельно  в периметре  каждой , поэтому сумма периметров всех  четырех меньших прямоугольников больше периметра исходного с периметром 2*(18+16)
1) 34*4>2*34
2) 40*4> 2*34

Answer 2

Problem Analysis

We are given a rectangle ABCD that has been divided into four smaller rectangles with equal perimeters. We are also given that AB = 18 cm and BC = 16 cm. We need to find the lengths of the sides of the other rectangles.

Solution

Let's denote the lengths of the sides of the smaller rectangles as a, b, c, and d. Since the perimeters of the four smaller rectangles are equal, we can set up the following equation:

2(a + b) + 2(c + d) = 2(AB + BC) Substituting the given values AB = 18 cm and BC = 16 cm into the equation, we have:

2(a + b) + 2(c + d) = 2(18 + 16) 2(a + b) + 2(c + d) = 2(34) a + b + c + d = 34 Since the perimeters of the four smaller rectangles are equal, the sum of the lengths of their sides must also be equal. Therefore, we can write:

a + b = c + d Substituting this equation into equation we have:

2(c + d) + 2(c + d) = 34 4(c + d) = 34 c + d = 34/4 c + d = 8.5 Now, we have two equations:

a + b = c + d c + d = 8.5

We can solve these equations to find the lengths of the sides of the other rectangles.

Let's solve for a and b in terms of c:

a = c + d - b b = c + d - a

Substituting these equations into the equation a + b = c + d, we have:

(c + d - b) + (c + d - a) = c + d 2c + 2d - a - b = c + d c + d - a - b = 0 a + b = c + d

Since a + b = c + d, we can conclude that a = c and b = d.

Therefore, the lengths of the sides of the other rectangles are:

a = c = 8.5/2 = 4.25 cm b = d = 8.5/2 = 4.25 cm

So, the lengths of the sides of the other rectangles are 4.25 cm and 4.25 cm.

Answer

The lengths of the sides of the other rectangles are 4.25 cm and 4.25 cm.